Non Verbal Reasoning · Reflections, Folding & Cutting
Paper Cutting — Questions & Answers
Paper cutting questions fold a sheet and cut pieces from its edges, corners or middle, then ask for the opened sheet. Cuts on a folded edge become whole shapes; cuts on the outer edge leave notches.
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How to approach
Every cut goes through all the layers, so it appears once per layer when the sheet is opened.
Mirror each cut across every fold line, starting with the last fold.
A cut on the outer edge or a corner leaves a notch in the sheet's outline, not a hole.
5 solved Paper Cutting questions
A rectangular sheet is folded as shown (the dashed part is folded over in the direction of the arrow), then cut where marked on the last figure. Which figure shows the sheet when it is opened out?
Solution — answer C
The paper is folded 3 times, so it has 8 layers and every cut goes through all of them: it appears 8 times on the opened sheet, mirrored across every fold line. A cut on a folded edge opens into one full shape across that crease; a cut on the outer edge or a corner leaves a notch in the sheet's outline.
4 steps · reveal one at a timeStep 1: Count the folds
First, count how many times the sheet is folded. The problem implies it is folded 3 times. This means there are 23=8 layers of paper where the cuts are made.
Step 2: Effect of cuts
Every cut goes through all 8 layers. When the sheet is opened, each cut will appear 8 times, mirrored across each fold line. This creates a symmetrical pattern.
Step 3: Types of cuts
A cut made on a folded edge will open out into a complete shape across that crease. A cut on an outer edge or a corner will result in a notch or indentation along the sheet's final outline.
Step 4: The answer
So the answer is (C) Figure C, because it correctly shows the pattern of 8 mirrored cuts, with specific cuts forming full shapes or notches based on their original position on the folded sheet.
A square sheet is folded as shown (the dashed part is folded over in the direction of the arrow), then cut where marked on the last figure. Which figure shows the sheet when it is opened out?
Solution — answer C
The paper is folded twice, so it has 4 layers and every cut goes through all of them: it appears 4 times on the opened sheet, mirrored across every fold line. A cut on a folded edge opens into one full shape across that crease; a cut on the outer edge or a corner leaves a notch in the sheet's outline.
4 steps · reveal one at a timeStep 1: Count the Layers
The problem describes a square sheet folded twice. Each fold doubles the paper's thickness. This means that when the cuts are made, they will pass through 2×2=4 layers of paper.
Step 2: Effect of Cuts
Since each cut goes through 4 layers, it will create four identical shapes when the paper is unfolded. These shapes will be mirrored across the original fold lines, creating a symmetrical pattern.
Step 3: Identify Cut Types
A cut made on a folded edge will open out into a full, complete shape across that crease. In contrast, a cut made on an outer edge or a corner of the folded paper will result in a notch or an indentation on the final sheet's outline.
Step 4: The answer
So the answer is (C) Figure C. This figure correctly shows the resulting pattern with cuts appearing 4 times, mirrored across the fold lines, and distinguishing between cuts on folded edges and outer edges.
A circular sheet is folded as shown (the dashed part is folded over in the direction of the arrow), then cut where marked on the last figure. Which figure shows the sheet when it is opened out?
Solution — answer A
The paper is folded once, so it has 2 layers and every cut goes through all of them: it appears 2 times on the opened sheet, mirrored across every fold line. A cut on a folded edge opens into one full shape across that crease; a cut on the outer edge or a corner leaves a notch in the sheet's outline.
4 steps · reveal one at a timeStep 1: Understand the fold
The circular sheet is folded once. This means that when the cut is made, it passes through two layers of paper. Each cut will therefore appear twice on the final opened sheet.
Step 2: How cuts appear
Every cut made on the folded paper will appear two times on the opened sheet. These two appearances will be mirrored across the original fold line, showing a symmetrical pattern.
Step 3: Special cut types
A cut made on a folded edge will open out into one full, continuous shape across that crease. Cuts made on an outer edge or a corner will create a notch or indentation in the sheet's overall outline.
Step 4: The answer
So the answer is (A) Figure A. This figure correctly shows the result of the cuts, with each cut appearing twice and mirrored, and any cuts on folded edges forming complete shapes.
A square sheet is folded as shown (the dashed part is folded over in the direction of the arrow), then cut where marked on the last figure. Which figure shows the sheet when it is opened out?
Solution — answer D
The paper is folded twice, so it has 4 layers and every cut goes through all of them: it appears 4 times on the opened sheet, mirrored across every fold line. A cut on a folded edge opens into one full shape across that crease; a cut on the outer edge or a corner leaves a notch in the sheet's outline.
4 steps · reveal one at a timeStep 1: Layers after folding
The square sheet is folded twice. This means that any cut made on the last figure will go through all 4 layers of the paper.
Step 2: Cuts are mirrored
Because there are 4 layers, each cut will appear 4 times on the opened sheet. These appearances are mirrored across every fold line created by the folding process.
Step 3: Types of cuts
A cut made on a folded edge will open out into a full shape across that crease. However, a cut made on an outer edge or a corner will simply leave a notch in the sheet's outline.
Step 4: The answer
So the answer is (D) Figure D. This figure correctly shows the cuts replicated four times and mirrored across the fold lines, with specific shapes resulting from cuts on folded edges and notches from cuts on outer edges.
A square sheet is folded as shown (the dashed part is folded over in the direction of the arrow), then cut where marked on the last figure. Which figure shows the sheet when it is opened out?
Solution — answer A
The paper is folded twice, so it has 4 layers and every cut goes through all of them: it appears 4 times on the opened sheet, mirrored across every fold line. A cut on a folded edge opens into one full shape across that crease; a cut on the outer edge or a corner leaves a notch in the sheet's outline.
4 steps · reveal one at a timeStep 1: Count paper layers
The square sheet is folded twice. This means that when a cut is made, it will pass through 2×2=4 layers of paper. Each cut will therefore be replicated four times when the sheet is opened.
Step 2: Understand cut mirroring
Because the paper is folded, each cut will appear 4 times on the opened sheet. These appearances will be mirrored across every fold line, creating a symmetrical pattern from the original cuts.
Step 3: Identify cut types
A cut made on a folded edge will open out into a complete shape across that crease. In contrast, a cut made on an outer edge or a corner of the folded paper will result in a notch or an indentation in the final sheet's outline.
Step 4: The answer
So the answer is (A) Figure A. This figure correctly shows the four mirrored repetitions of the cuts, with cuts on folded edges forming full shapes and cuts on outer edges forming notches, consistent with the folding and cutting process.
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